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Solved: A 100-g toy car is propelled by a compressed
Chapter 7, Problem 20(choose chapter or problem)
A \(100-\mathrm{g}\) toy car is propelled by a compressed spring that starts it moving. The car follows the curved track in Figure \(7.39\). Show that the final speed of the toy car is \(0.687 \mathrm{~m} / \mathrm{s}\) if its initial speed is \(2.00 \mathrm{~m} / \mathrm{s}\) and it coasts up the frictionless slope, gaining \(0.180 \mathrm{~m}\) in altitude.
Figure \(7.39\) A toy car moves up a sloped track. (credit: Leszek Leszczynski, Flickr)
Equation Transcription:
Text Transcription:
100-g
7.39
0.687 m/s
2.0 m/s
0.180 m
Questions & Answers
QUESTION:
A \(100-\mathrm{g}\) toy car is propelled by a compressed spring that starts it moving. The car follows the curved track in Figure \(7.39\). Show that the final speed of the toy car is \(0.687 \mathrm{~m} / \mathrm{s}\) if its initial speed is \(2.00 \mathrm{~m} / \mathrm{s}\) and it coasts up the frictionless slope, gaining \(0.180 \mathrm{~m}\) in altitude.
Figure \(7.39\) A toy car moves up a sloped track. (credit: Leszek Leszczynski, Flickr)
Equation Transcription:
Text Transcription:
100-g
7.39
0.687 m/s
2.0 m/s
0.180 m
ANSWER:
Solution 20PE
The toy car moves up the slope and gains a height. This gain in height will result in the change in potential energy for the toy. At the start of its motion, the toy car will have a greater velocity. But as it will continue to move upward, it will slow down. So, there will be a change in its kinetic energy. We are required to calculate the speed of the toy when it reaches the height of 0.180 m.
Step 1 of 2
Initial height of the toy is zero. So, the initial potential energy of the toy is also zero.
The initial speed of the toy m/s
Final height of the toy m
We are required to show that the final speed of the toy is 0.687 m/s.